On universal covers for four-dimensional sets of a given diameter

Details On universal covers for four-dimensional sets of a given diameter On universal covers for four-dimensional sets of a given diameter

2010-07-15

arxiv.org/abs/1007.2520v2

Mathematics

Metric Geometry

5 pages

Scientific paper

Makeev proved that among centrally symmetric four-dimensional polytopes, with more than twenty facets and circumscribed about the Euclidean ball of diameter one, there is no universal cover for the family of unit diameter sets. In this paper we examine the converse problem, and prove that each centrally symmetric polytope, with at most fourteen facets and circumscribed about the Euclidean ball of diameter one, is a universal cover for the family of unit diameter sets.

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